A few possibilities:
1. She did die in that flat
1.a and Eddie correctly alerted to her cadaver odour.
1.b She did die in the flat, and Eddie coincidentally alerted to some irrelevant human decomposition scent.
2. She left the flat alive, and Eddie's alerts were to some irrelevant human decomposition scent
The problem I have is that a) no evidence was found, b) quite apart from the forensics people, etc., the flat had been occupied by 4 lots of people, the last lot leaving just one week prior to the dog inspection, and AFAIK there aren't any witness statements from any of them in the PJ files, c) nowhere is it stated clearly exactly what "items he is trained to find" (cf the car video) actually includes or excludes.
Can it be excluded that he sniffed the scent of a bloody sock or plaster left lying around for a while by one of the post-disappearance occupants prior to removal? The PJ did organise interviews from pre-disappearance occupants, but apparently none of the post- ones? Wouldn't it have been logical to do so?
If scent tends to cling to porous materials... The flat was used for holiday rentals. Did anyone think to turn over the mattress?